Changeset e9f5b2 in git


Ignore:
Timestamp:
Jul 7, 2009, 6:29:58 PM (15 years ago)
Author:
Viktor Levandovskyy <levandov@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'd25190065115c859833252500a64cfb7b11e3a50')
Children:
642e65dac97b59e7fbbbcd4fa0e29e65a4ae0853
Parents:
6d5f07fc0cb4ce2f4c48acf8a4816a6c809a5175
Message:
*levandov: documentation and assumptions reworked


git-svn-id: file:///usr/local/Singular/svn/trunk@11956 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/ncdecomp.lib

    r6d5f07 re9f5b2  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: ncdecomp.lib,v 1.14 2009-04-09 12:04:42 seelisch Exp $";
     2version="$Id: ncdecomp.lib,v 1.15 2009-07-07 16:29:58 levandov Exp $";
    33category="Noncommutative";
    44info="
     
    77
    88OVERVIEW:
    9 This library presents algorithms for the  central character
    10 decomposition of a module, i.e. a decomposition into generalized weight modules with respect to the center. Based on ideas of O. Khomenko and V. Levandovskyy (see the article [L2] in the References for details).
     9@* This library presents algorithms for the central character decomposition of a module,
     10@* i.e. a decomposition into generalized weight modules with respect to the center.
     11@* Based on ideas of O. Khomenko and V. Levandovskyy (see the article [L2] in the
     12@* References for details).
    1113
    1214PROCEDURES:
     
    1921  LIB "ncalg.lib";
    2022  LIB "primdec.lib";
    21 ///////////////////////////////////////////////////////////////////////////////
     23  LIB "central.lib";
     24
     25///////////////////////////////////////////////////////////////////////////////
     26
     27proc testncdecomplib()
     28{
     29  example CentralQuot;
     30  example CentralSaturation;
     31  example CenCharDec;
     32  example IntersectWithSub;
     33}
     34
    2235static proc CharKernel(list L, int i)
    2336{
     
    106119RETURN:  module
    107120PURPOSE: compute the central quotient M:G
    108 THEORY:  for an ideal G of the center of an algebra and a submodule M of A^n, the central quotient of M by G is defined to be
     121THEORY:  for an ideal G of the center of an algebra and a submodule M of A^n,
     122@* the central quotient of M by G is defined to be
    109123@* M:G  :=  { v in A^n | z*v in M, for all z in G }.
    110124NOTE:    the output module is not necessarily given in a Groebner basis
     
    112126EXAMPLE: example CentralQuot; shows examples
    113127"{
     128/* check assupmtion. Elt's of G must be central */
     129  if (! inCenter(G) )
     130  {
     131    ERROR("ideal in the 2nd argument is not in the center of the base ring!");
     132  }
    114133  int i;
    115134  list @L;
     
    147166EXAMPLE: example CentralSaturation; shows examples
    148167"{
     168/* check assupmtion. Elt's of T must be central */
     169  if (! inCenter(T) )
     170  {
     171    ERROR("ideal in the 2nd argument is not in the center of the base ring!");
     172  }
    149173  option(redSB);
    150174  option(redTail);
     
    209233    Center = #;
    210234  }
     235
     236/* check assupmtion. Elt's of G must be central */
     237  if (! inCenter(Center) )
     238  {
     239    ERROR("ideal in the 2nd argument is not in the center of the base ring!");
     240  }
     241
    211242// M = A/I
    212243//1. Find the Zariski closure of Supp_Z M
     
    335366"USAGE:  IntersectWithSub(M,Z),  M an ideal, Z an ideal
    336367ASSUME: Z consists of pairwise commutative elements
    337 RETURN:  ideal, of two-sided generators, not a Groebner basis
     368RETURN:  ideal of two-sided generators, not a Groebner basis
    338369PURPOSE: computes the intersection of M with the subalgebra, generated by Z
    339370NOTE:    usually Z consists of generators of the center
     
    358389  }
    359390  // returns a submodule of M, equal to M \cap Z
    360   // correctness: Z should consists of pairwise
     391  // assume/correctness: Z should consists of pairwise
    361392  // commutative elements
    362393  int nz = size(Z);
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